A small example on how to use the same kind of system for multiple contexts in Entitas 0.37.0(+) while making usage of a shared component.

CleanUpGameObjectSystem.cs

using System.Collections.Generic;
using Components.GameObjects;
using Components.Miscellaneous;
using Entitas;
using Entitas.Unity.VisualDebugging;
using EntitasHelpers;
using JetBrains.Annotations;

public sealed class CleanUpGameObjectSystem<TEntity> : ReactiveSystem<TEntity> where TEntity : class, IEntity, new()
{
    private readonly Context<TEntity> _context;
    private IMatcher<TEntity> _triggerMatcher;

    public CleanUpGameObjectSystem([NotNull] Context<TEntity> context) : base(context)
    {
        _context = context;
    }

    protected override Collector<TEntity> GetTrigger(IContext<TEntity> context)
    {
        _triggerMatcher = Matcher<TEntity>.AllOf(context.IndicesOfComponentTypes(new[]
        {
            typeof(DestroyRequestedComponent),
            typeof(GameObjectComponent)
        }));
        return context.CreateCollector(_triggerMatcher);
    }

    protected override bool Filter(TEntity entity) => _triggerMatcher.Matches(entity);

    protected override void Execute(List<TEntity> entities)
    {
        foreach (var entity in entities)
        {
            var gameObjectComponent = (GameObjectComponent)entity.GetComponent(_context.IndexOfComponentType<TEntity, GameObjectComponent>());
            gameObjectComponent.Value.DestroyGameObject();
        }
    }
}

For the implementations of the methods IndicesOfComponentTypes and IndexOfComponentType on IContext see this other gist.